Am I allowed to make homemade sushi on shabbos? Is there anything impermissible about flattening the rice on seaweed and assembling the roll?
Yes,sushi may be made on Shabbos.
Boneh: The comparison to Megaben, cheese making which is forbidden because of Boneh is difficult. Cheese making creates an entirely new entity from it’s ingredients, merely shaping or clumping food together is much less significant as nothing new was made. The Kitzur Shlchan Aruch does prohibit something similar. His source is the Magen Avraham 340:17 who questions why making date cakes or stringing figs is a problem of Meamer and not Boneh. To this he answers boneh would only be when it is done to beautify the final product. A careful reading of the Magen Avraham reveals he was only bothered by the stringing of figs which to an extent is a new creation, not making date cakes. Sushi would seem to be most similar to date cakes , clumping and slightly molding into a shape which is explicit in Shulachan Aruch that there is no problem of Boneh. This is not done for beauty per say, rather this is the shape of the food and the way to get the ingredients together.
Makeh Bpatish: there is a debate in the achronim if this prohibition exists by food, the opinion of the 318:4 is that it does not. Even according to the Pri Megadim this prohibition is only when something is done to food that was otherwise unfit for consumption, such as rinsing off salty meat even with cold water. Sushi is perfectly edible before it is all rolled together.
Tofer: The melacha of Tofer is not applicable to sushi. There is no binding agent used, moistness creates a slight stickiness which holds the food together in a loose way which is not intended to last for more than a short time. See Rama 317:3 that there is no problem of tefira in such a manner.